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HW01-solutions

# HW01-solutions - handa(nh5757 HW01 meth(55830 This...

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handa (nh5757) – HW01 – meth – (55830) 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Below is the graph of a function f . 2 4 6 - 2 - 4 - 6 2 4 6 8 - 2 - 4 Use the graph to determine lim x → - 5 f ( x ). 1. lim x → - 5 f ( x ) = 6 2. lim x → - 5 f ( x ) = 9 3. lim x → - 5 f ( x ) = 3 correct 4. lim x → - 5 f ( x ) does not exist 5. lim x → - 5 f ( x ) = 4 Explanation: From the graph it is clear the f has both a left hand limit and a right hand limit at x = - 5; in addition, these limits coincide. Thus lim x → - 5 f ( x ) = 3 . 002 10.0points When f is the function defined by f ( x ) = braceleftbigg 5 x - 1 , x < 1 , 4 x - 1 , x 1 , determine if lim x 1 - f ( x ) exists, and if it does, find its value. 1. limit = 5 2. limit = 3 3. limit = 4 correct 4. limit does not exist 5. limit = 2 6. limit = 6 Explanation: The left hand limit lim x 1 - f ( x ) depends only on the values of f for x > 2. Thus lim x 1 - f ( x ) = lim x 1 - 5 x - 1 .

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